[en] A new "self-calibrated" statistical analysis method has been developed for reducing nulling interferometry data. The idea is to use the statistical distributions of the fluctuating null depths and beam intensities to retrieve the astrophysical null depth (or equivalently the object's visibility) in the presence of fast instrumental fluctuations. The approach yields an accuracy much better (at least ten times) than is presently possible with standard data reduction methods, because the null depth accuracy is no longer limited by the magnitude of the phase and intensity errors but by uncertainties on their probability distributions. This approach was tested on the sky with the two-aperture fiber nulling instrument mounted on the Palomar Hale telescope. Using our new data analysis approach alone - and no observations of calibrators - , we find that astrophysical null depths lower than 0.001 can be reliably measured in the near infrared, with error bars as low as a few 10^-4. This statistical analysis is not specific to our instrument and may be applicable to other interferometers. Therefore I'll also present the application of this method to the measurement of Cepheids angular diameters at the VLTI with a sensitivities down to ~60µas.